Coon amplitude equals 3d N=2 half-index of XYZ model with boundary conditions; IR flow gives Veneziano amplitude, and elliptic completion of q^ST yields a meromorphic positive version.
Lectures on K-theoretic computations in enumerative geometry
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abstract
These are notes from my lectures on quantum K-theory of Nakajima quiver varieties and K-theoretic Donaldson-Thomas theory of threefolds given at Columbia and Park City Mathematics Institute. They contain an introduction to the subject and a number of new results. In particular, we prove the main conjecture of arXiv:hep-th/0412021 and the conjecture of arXiv:1404.2323 in the simplest case of reduced smooth curves. We also prove the the absence of quantum corrections to the capped vertex with descendents for sufficiently large framing (and polarization), which is a property we call large framing vanishing. The shift operators for minuscule shift are shown to be given by qKZ operators, which is a K-theoretic analog of the result of arXiv:1211.1287.
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A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.
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Meromorphic amplitudes from 3-dimensional supersymmetry
Coon amplitude equals 3d N=2 half-index of XYZ model with boundary conditions; IR flow gives Veneziano amplitude, and elliptic completion of q^ST yields a meromorphic positive version.
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Motivic Segre classes of Schubert cells and the connective formal group law
A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.